20.5.2 Infinity and NaN

IEEE 754 floating point numbers can represent positive or negative
infinity, and NaN (not a number). These three values arise from
calculations whose result is undefined or cannot be represented
accurately. You can also deliberately set a floating-point variable to
any of them, which is sometimes useful. Some examples of calculations
that produce infinity or NaN:

1/0 = &infin;log (0) = -&infin;sqrt (-1) = NaN

When a calculation produces any of these values, an exception also
occurs; see FP Exceptions.

The basic operations and math functions all accept infinity and NaN and
produce sensible output. Infinities propagate through calculations as
one would expect: for example, 2 + &infin; = &infin;,
4/&infin; = 0, atan (&infin;) = &pi;/2. NaN, on
the other hand, infects any calculation that involves it. Unless the
calculation would produce the same result no matter what real value
replaced NaN, the result is NaN.

In comparison operations, positive infinity is larger than all values
except itself and NaN, and negative infinity is smaller than all values
except itself and NaN. NaN is unordered: it is not equal to,
greater than, or less than anything, including itself. x ==
x is false if the value of x is NaN. You can use this to test
whether a value is NaN or not, but the recommended way to test for NaN
is with the isnan function (see Floating Point Classes). In
addition, <, >, <=, and >= will raise an
exception when applied to NaNs.

math.h defines macros that allow you to explicitly set a variable
to infinity or NaN.

Macro: floatINFINITY

An expression representing positive infinity. It is equal to the value
produced by mathematical operations like 1.0 / 0.0.
-INFINITY represents negative infinity.

You can test whether a floating-point value is infinite by comparing it
to this macro. However, this is not recommended; you should use the
isfinite macro instead. See Floating Point Classes.

This macro was introduced in the ISO C99 standard.

Macro: floatNAN

An expression representing a value which is “not a number”. This
macro is a GNU extension, available only on machines that support the
“not a number” value—that is to say, on all machines that support
IEEE floating point.

You can use ‘#ifdef NAN’ to test whether the machine supports
NaN. (Of course, you must arrange for GNU extensions to be visible,
such as by defining _GNU_SOURCE, and then you must include
math.h.)

IEEE 754 also allows for another unusual value: negative zero. This
value is produced when you divide a positive number by negative
infinity, or when a negative result is smaller than the limits of
representation.